Parabolic (3,5,6)-distributions and Gl(2)-structures

We consider rank 3 distributions with growth vector (3,5,6). The class of such distributions splits into three subclasses: parabolic, hyperbolic and elliptic. In the present paper, we deal with the parabolic case. We provide a classification of such distributions and exhibit connections between them and Gl(2)-structures. We prove that any Gl(2)-structure on three and four dimensional manifold can be interpreted as a parabolic (3,5,6)-distribution.